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Move your content to a new Mac - Apple Support
Synchronizing data between devices is a complex issue, and there's no really ideal solution. This comment is an oversimplification.
Mail can be synchronized by storing it on a mail server that uses the IMAP protocol, such as iCloud. The mail stays on the server, so it's automatically in sync with all mail clients.
Several other kinds of data can be synced via iCloud, such as calendars, iWork documents, photos, Safari tabs and bookmarks, and keychains. Some third-party applications can also sync with iCloud, but not many. iCloud is easy to use, for the most part. The drawbacks of using it are, first, that it doesn't sync everything; and second, that some of your private information will be in the hands of strangers. Read the iCloud feature list and privacy notice carefully before deciding whether or how to use it. There should be no privacy concerns with iCloud keychain, because the data is encrypted end-to-end and is not accessible to anyone at Apple—but you have to take Apple's word for that.
A more comprehensive solution, and one that doesn't raise any privacy issues, is to set up an OS X Server on your network and create mobile accounts on your other Macs. You will then be able to synchronize all files in the home folder automatically at logout, or at any other time manually. The main drawback here is that OS X Server would be hard for most non-technical users to set up and maintain. Another is that the synchronization only works with Macs, not mobile devices.
Third-party software such as Unison can also be used to synchronize files over a network. Unison is free, but it's not easy to set up in a way that doesn't lead to conflicts when files are modified on different devices between synchronizations. To synchronize more than two Macs in this way, you'll want to use one as the master, and sync between it and the others.